Number worksheet — GCSE Higher

1.Write down the exact decimal value of the fraction 1/6.

2.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

3.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

4.Write 0.06 as a fraction in its simplest form.

5.Find the missing number: ▢ ÷ 15 = 24

6.Simplify √8 + √18, giving your answer in the form k√2.

7.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

8.Write 7/12 as a decimal, showing clearly which digit is recurring.

9.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

10.Work out −(−3)⁴ + (−3)³

11.Work out ⁴√16

12.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

13.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

14.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

15.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.